(5a+8)(4a-10)=18

Solution for (5a+8)(4a-10)=18 equation:

(5a+8)(4a-10)=18

We move all terms to the left:

(5a+8)(4a-10)-(18)=0

We multiply parentheses ..

(+20a^2-50a+32a-80)-18=0

We get rid of parentheses

20a^2-50a+32a-80-18=0

We add all the numbers together, and all the variables

20a^2-18a-98=0

a = 20; b = -18; c = -98;
Δ = b2-4ac
Δ = -182-4·20·(-98)
Δ = 8164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8164}=\sqrt{4*2041}=\sqrt{4}*\sqrt{2041}=2\sqrt{2041}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{2041}}{2*20}=\frac{18-2\sqrt{2041}}{40}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{2041}}{2*20}=\frac{18+2\sqrt{2041}}{40}
$